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As the sample size (n) increases, the variation in the sampling distribution of the sample means increases.

Professors in the Department of Animal Sciences want to estimate the average length of time it takes students to complete a class project correct to within 5 hours with a 98% level of confidence.  Determine the sample size needed to estimate the average length of time required to complete the project to within 5 hours with a 98% level of confidence.  They do not know the standard deviation of the times, but they remember that last year the shortest amount of time needed to complete the project was 5 hours and the longest amount of time was 29 hours.

The owner of Get-A-Way Travel has recently surveyed a random sample of 385 customers of the agency.  He would like to determine if the mean age of the agency’s customers is over 31 years.  If so, he plans to alter the destination of their special cruises and tours.  If not, no changes will be made.  He therefore wants to test:    Ho:  μ = 31 years    Ha:  μ > 31 years If he concludes that the mean age is not over 31 years when in fact it is over 31 years, he makes a ________ error.

Find the variance of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.60.

The probability distribution for the number X out of 5 randomly selected dentists who use laughing gas is shown below:                                                                                                                            X               0                1                 2                  3                4                  5         P (X)     0.0102       0.0768        0.2304         0.3456        0.2592         0.0778      Find the mean number of dentists out of 5 who use laughing gas.

The heights in inches of young growing trees were measured at a nursery and used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf: Stem                       Leaves                                     3               2     4 4               0     3     4     5     7     8     9 5               0     1     2     3     4     5 6               1     2     5     6     7 7               0     1 8 9               8 Based on the stem-and-leaf display, the upper quartile for this set of tree heights is __________ inches.

We want to test the hypothesis that the mean yield of a particular variety of corn is less than 150 bushels per acre.  Therefore, we obtain the yields of a random sample of 20 corn fields in which this variety was planted. The average yield of the sample of fields was 140 bushels per acre with a standard deviation of 10 bushels per acre.  We want to test:    Ho:  μ = 150 bushels/acre    Ha:  μ < 150 bushels/acre using a significance level (α) = 0.10. Should we reject or not reject the null hypothesis?  Why?

The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the range for the grades of these 8 students.

Tests for the differences in the mean levels of the main effects in a factorial experiment are relevant only when the factors do not interact.

Find the variance of a binomial probability distribution with a sample size of n = 25 and a probability of success of 0.30.